Joint modeling of longitudinal change of fasting blood sugar and systolic blood pressure with survival time to death among hypertension patients

Hypertension is a universal public health challenge and a leading modifiable risk factor for cardiovascular disease and death. It is also called high blood pressure, described by two measured quantities systolic blood pressure (SBP) 140 mmHg or greater and diastolic blood pressure (DBP) 90 mmHg or greater. As the result, this study aims to use the joint model application to identify the factors that affect longitudinal changes in fasting blood sugar, SBP, and survival time to death of hypertension patients and their associations admitted to the Arba Minch General Hospital. We considered a total of 354 random samples of hypertension patients who had under follow-up at Arba Minch general hospital from January 2012 to February 2020. Among 2330 hypertension patients under follow-up, 354 were selected with a simple random sampling technique, and data was collected from the patient’s medical cards. After evaluating the longitudinal data with a linear mixed model and the baseline data with Cox proportional models, the joint models of both sub-models were assessed in R software version 4.2. According to the findings, the association between longitudinal changes (FBS, SBP, and time to death in hypertension patients was statistically significant. Ages, place of residence, lifestyle change, stages of hypertension, blood cholesterol level, related diseases, adherence to treatment, family history of hypertension patients, and DBP at baseline were associated factors that affect survival time and longitudinal measurement of FBS and SBP of the patients. The computed association parameters revealed subject-specific values. The subject-specific linear time slope of FBS and SBP was negatively related to the hazard rate of time to death of hypertension patients in Arba Minch general hospital. To reduce the risk of hypertension in patients, health professionals, governmental organizations, and non-governmental organizations must promote the implementation of community-based screening programs for early detection of hypertension.

Study design. To achieve the study's objective, a retrospective study was done to collectimportant information from the medical files of patients with hypertension.
Data source. To achieve the study's objective, a retrospective study was done to collect important information from the medical files of patients with hypertension. The data for this study were collected from patients' medical cards, which contained epidemiological, laboratory, and clinical information regarding the patients who had been followed up at Arba Minch General Hospital from January 2012 to February 2020. The timing of the death of hypertension patients was the survival endpoint of interest.The research proposal of this study was checked and approved by Arba Minch University department of statistics and ethical clearance committee of the University. So, Informed consent has been waived by the ethical committee of the University. All study procedures were performed following relevant guidelines and regulations laid down by the Committee.
Ethics declarations. The letter of ethical clearance was obtained from the institutional review board of Arba Minch University, and Arba Minch General Hospital gave permission to collect data of hypertension patients from recorded cards. For the purpose of confidentiality, there were no links with individual patients and all data had no personal identifier and were kept confidential and therefore Informed consent has been waived by Arba Minch University ethical committee. Study variables. The longitudinal changes in systolic blood pressure, fasting blood sugar and the survival time of hypertension patients after initiating medication were the study's response variables. The longitudinal measurements were measured repeatedly over time for each hypertension patient under follow up. The survival time was measured time in months of a patient to the associated death event. Moreover, it is time to death event of the patient under the follow-up.
The Explanatory variables considered in this study were: observed time, square of observed time gender, base line age, place of residence, alcohol use, Khat intake, tobacco use, status of stress, stages of hypertension disease, life style change, blood cholesterol level, adherence to treatment, related diseases, family history of hypertension patients, DBP, diabetes of mellitus status were all factors considered. Statistical models. Statistical models. Different statistical models such as the joint model, the longitudinal linear mixed-effect (LME) model; and the event time model were investigated. The analysis was carried out using R software version 4.2.A linear mixed-effect model for longitudinal data and a Cox proportional hazard (PH) model for survival data, with an association parameter, show the effect of longitudinal measurement on hypertension patients survival time to death. Linear mixed effect model for longitudinal measurements. The SBP and FBS measurements were collected longitudinally from the same individuals throughout several observation times. The LME model is a parametric linear model for longitudinal or repeated measurement data that quantifies the associations between a continuous dependent variable and a large number of predictor factors. It builds on the traditional linear regression model by accounting for both fixed and random factors. Subject-specific effects are included in the random effect 8 .
Let y ijk represent the jth observation of the kth outcome variable for the i th subject, where: i = 1, 2…354, j = 1, 2… n i and also, K = 1, 2 the vector ( y 1ik + y 2ik + · · · + y nik ) T represents the n ik observations of the kresponse variable from the ith subject and vector ( y 1k , y 2k ,…y nik ) T represent the N k observation for the kth response variable across all response variables and subjects, finally the vector ( y 1 y 2 , y 3 ,…y n ) T represents the observations across all response variables and subjects shown in (Eq. 1) 9 .
whereY ijk (t) is the corresponding true underlying longitudinal measures of the kth biomarker for the i th subject; jth observation, which is the ( n i ) dimensional response matrix for subject i 1 ≤ i ≤ N, N is the number of subjects,X ik (t) and Z ik (t) were the 1xp and 1xr(0 < r ≤ p) design matrix of fixed and random effects, respectively.
(1) www.nature.com/scientificreports/ The px1 and rx1 vectors of corresponding fixed and random effects parameters are β k and b ik ; m ik denotes the true, unobserved value of longitudinal response; and ε ik (t) the measurement error.
Survival sub model. For the survival sub-model, we propose Cox PH and event time is the time elapsed up to the occurrence of an event of interest, which is death, given that it has not previously occurred yet. Let T * i and C i be the true event time and censoring time, respectively for subject i . The observed event time is defined as = min ( T * i , C i ) and the event indicator δi = I ( T * i ,C i ). Assuming that the hazard function depends on some functions of the true longitudinal measures m ik (t) and the baseline covariates, the hazard function 10 .
To achieve this we introduce the term m ik (t) that denotes the true and unobserved value of the longitudinal outcome at time t . Note that m ik (t) is different from y ik (t) with the latter being the contaminated with measurement error value of the longitudinal outcome at time t . To quantify the strength of the association between m ik (t) and the risk for an event, a straightforward approach is to postulate a PH models of the form (Eq. 2):

Results and discussions
In this study, among 354 hypertension patients 54.52% were females and 45.48% were males. The majority of the patients were detected at the age of > 50. That means 51.13% patients older than 50 years and 48.87% the patients younger 50 years. Regarding the residence area of the patients, about 63% of patients were living in urban areas, and 37% of patients resided in rural areas with death proportions of 11.66%, and 6.87% respectively. From a total of 354 hypertension patients, 35 (10%) died, while 319 (90%) were censored ( Table 1).
The baseline average mean of FBS, SBP, and DBP of patients were 132.47, 162.12 and 99.93, with a standard deviation of 54.91, 25.52 and 13.91, respectively; which means that an average SBP and DBP at baseline were different from the range of normal human blood pressure ( Table 2).
Heterogeneous first order autoregressive variance-covariance has lowered Akaike information criteria (AIC), and Bayesian information criteria (BIC) values than those in other covariate structure, indicating that heterogeneous first order autoregressive variance-covariance is the best fit for our data when compare to the other covariance structures for the longitudinal change in SBPand FBSof hypertension data ( Table 3).
The model with random intercept and slope was chosen as the most parsimonious model for the LME model for the longitudinal change of SBPandFBSdue to lower values of AIC and BIC for both FBS and SBP ( Table 4).
The association parameters r 1 and r 2 are statistically significant ( r 1 = − 1.05 with p-value < 0.009 and r 2 = −0.035 ) with p-value < 0.001 respectively. The significance of the association parameter suggests that there is a strong dependence (association) between longitudinal changes (SBP and FBS) with survival time of hypertension patients.
The joint model analysis in Table 5 below showed that the longitudinal changes of (SBP and FBS) were significantly associated with observed time, square of observed time, place of residence, alcohol use, life style change, tobacco use, age, blood cholesterol level, adherence to treatment, family history of hypertension patient. Furthermore, in the survival sub-model, the survival time of hypertension patients was related to baseline age, place of residence, life-style change, Khat intake, stages of hypertension diseases, blood cholesterol level, related diseases, adherenceto treatment, family history of hypertension and diastolic blood pressure measurement at base line.
For instant, in a survival sub-model, all the estimated average regression coefficients, hazard ratio and up values off baseline age, lifestyle change, Khat use, blood cholesterol level and adherence to treatment are 0.27, HR = 1.027 (p < 0.002), 0.297, HR = 1.346 (p < 0.007), 0.17, HR = 1.18 (p < 0.002), 0.0183HR = 1.018 (p < 0.0015), and 0.221, HR = 1.247 (p < 0.001) were significant effect respectively at 5%level of significance (Table 5).These estimates show that, while an increase in age of the patients increases the hazard rate of death, patients who have no lifestyle change have higher hazard to death. Similar, patients who use Khat and tobacco have higher rates of death compared to patients who did not use Khat and tobacco. This shows that Khat and Tobacco negatively influence the survival time of hypertension patients.
The stages of hypertension disease increases (from normal stage to hypertensive crisis stage) the survival time of hypertension patients' decrease. And an increase in raised blood cholesterol level, poor adherence to treatment, related diseases, positive family history of hypertension patients, base line FBS level measurement, base line diastolic blood pressure measurement respectively increases hazard to death although the survival time of patient declines.

Discussion
The purpose of this study was to use the joint model application to identify the factors that affect longitudinal changes in SBP, FBS, and survival time to death of hypertension patients and their associations admitted to the Arba Minch General Hospital. In this study, the founding from the analysis of the survival sub-model shows that variables like age, alcohol use, Khat use, lifestyle change tobacco use, blood cholesterol level, family history, diabetic status, and stage of hypertension were significantly associated with survival time of the patients. The study revealed that the variables place of residence and observation time had significant associations with changes in SBP. This finding was similar to the finding in Jimma University specialized hospital, south-west Ethiopia reported that place of residence, and observation time have significant effects on change in SBP measurement 11 . Also, the current study reveals that the stage of hypertension, family history of adherence to treatment, related  13 .In this study, smoking tobacco, Khat use, and alcohol use were significantly associated with survival time of hypertension. The study reveals that patients who did not use alcohol did not use Khat and did not smoke tobacco had a better survival probability than those  indicated that alcohol use is a potential risk factor for hypertension, and they also found hypertension was significantly higher in individuals who use alcohol than in those who did not use it 14 . This study finds that there is a strong dependence between SBP, FBS, and survival time of hypertension patients at AMGH, and suggests that joint model analysis rather than separate model analysis for such kind of dependence outcomes, clinical and medical studies. These findings are agreed with previous researchers' findings [15][16][17] . In this study, the finding regarding the relationship between place of residence of patients and survival time until hypertension associated death was similar with finding in Addis Ababa Ethiopia reported that place of residence has a significant effect on hypertension patients' survival time 14 . Moreover, we found that a family history of hypertension disease was a statistically significant risk factor for death in hypertension patients; this finding is consistent with the findings of other researchers 18 . The current study found that age was related to the survival time of hypertension patients. This result is consistent with findings from a study in Ethiopia and Uganda 12,14 . Our study found that Khat intake was associated with the survival time of hypertension patients. These results are consistent with findings from a study 19 that identified that Khat chewing is one of the risk factors for hypertension mortality.

Conclusions
The linear mixed-effect model with subjective values of SBP and FBS was a good fit for the longitudinal changes in SBP and FBS evaluations in this investigation. At a 5% level of significance, the variables including observed time, square of observed time, age, place of residence, alcohol use, lifestyle change, tobacco use, blood cholesterol level, adherence to treatment, family history, and diastolic blood pressure were significantly associated with longitudinal measurement of (SBP and FBS) Joint models were used with the assumptions of a linear mixed effect model for the longitudinal change of (SBP and FBs) with survival time of hypertension patients data collected from AMGH. Model comparison was employed to select fitted model, Weibull parametric model was fitted model for survival analysis. In survival sub-model covariates: baseline age, place of residence, lifestyle change, Khat intake, stages of hypertension disease, blood cholesterol level, related diseases, adherence to treatment, family history, and baseline diastolic blood pressure measurement were significantly affect the survival time of hypertension patients at 5% level of significance. In joint model analysis, association parameters were significant at a 5% level of significance. Thisindicates that there is a strong dependence between longitudinal changes (SBP and FBS) and with survival time of patients. The negative sign of the estimated association parameter indicates longitudinal changes (SBP and FBS) measurementwere negatively associated with the survival time of the patients in the study area, implying lower values of the SBP and FBS measurements associated with better survival time of the patients. Based on the findings, we recommended that patients in societies who have positive family history should take action on early detection and prevention mechanisms as well as should be aware of the risk factors. Also for further improvements, the Policymakers, concerned bodies, and Arba Minch General Hospital should give more attention and intervention to identified risk factors in society, and Programs should design to improve the surveillance systems and implementations of community-based screening programs for early detection of hypertension are recommended.